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C₂×#26198 #6441805

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2808 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12)(13,17)(14,15)(16,18);(3,5,6,10)(4,7,8,9)(12,15)(16,17)(19,20)(21,23)(22,25)(24,26);(11,13,14,18)(12,16,15,17)(20,23)(21,26)(24,25);(4,8)(7,9)(12,15)(16,17)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349001);